1. Field
The following pertains to the fields of information storage and transfer, and more particularly to the field of Low Density Parity Check (LDPC) codes used to encode information for conveyance over a channel, such as an InterSymbol Interference (ISI) channel.
2. Description of Related Art
A “channel” is a term for a model of any system that conveys information through space and/or time, e.g., storage media and communication systems can be modeled as channels.
An InterSymbol Interference (ISI) channel refers to a type of distortion channel. Distortion refers to spreading and consequent overlap of individual elements of a signal to the degree that a receiver cannot reliably distinguish between individual signal elements. For example, a partial response magnetic recording channel is an ISI channel. The wireless fading channel, usually modeled as a tapped-delay-line is also an ISI channel.
Every channel has a capacity. As long as a data transmission rate is less than the channel capacity, it is possible to obtain a low-error rate system through the use of certain error correction codes. Low Density Parity Check (LDPC) Codes codes are known examples of good performance error correction codes that allow transmission rates close to channel capacity at realistic signal-to-noise ratios (SNR).
An LDPC code is a linear block code that can be defined by a parity check matrix with a small number of nonzero elements in each row and column. LDPC codes can be constructed over any Galois Field. For example, a binary LDPC code is defined over GF(2), in which “1” is the only nonzero element. LDPC codes can provide error protection for both data bits and for parity bits. For example, in one type of usage, a parity check matrix, H, defines an LDPC code, and can be for encoding the segments of information bits to produce codewords for storage/transmission on a channel. These codewords can be used to reconstruct the information bits in the presence of ISI.
Different types of LDPC codes exist, as do different ways of constructing such codes. One basic distinction among LDPC codes is whether the code's parity check matrix is constructed randomly or by a repeatable methodology. Taking into account further processing for considerations such as removal of 4-cycles from the parity check matrix, codes constructed randomly can perform as well or better than codes constructed by a repeatable methodology.
One way to generate a LDPC code is by using array codes. In some circumstances, array codes, when used as binary error correcting codes, have sparse parity check matrices that can be used as LDPC codes.
U.S. Pat. No. 6,895,547 (the '547 patent) discloses an array-code like parity check matrix H=[U|H2] at (9:20-25). H can be used to generate an LDPC codeword having kp bits from (k−j)p information bits, where the remainder of the bits, jp bits, are parity bits. U is a square upper triangular matrix of dimension jp×jp, while H2 is a sparse matrix of size jp×(k−j)p. P is a prime number that is equal to or greater than both j and k. The U portion of H produces the jp parity bits for the codeword. Each of the first p columns of U have column weights of 1, i.e., there is only 1 non-zero element in each column.
In some applications, the jp parity check bits are used in reproducing the (k−j)p information bits at a decoder, but are not, of themselves, retained. In such applications, the parity check bits are discarded after the information bits have been reproduced with sufficient accuracy. In other applications, the accuracy of the parity bits themselves can be important. Also, undetected errors in parity check bits can interfere with accurate determination of the information bits. Therefore, improvements to increase such reliability of the parity bits can be desirable.